Method of manufacturing lens array

ABSTRACT

A method of manufacturing a lens array according to the invention is presented wherein a first array of first lens-base elements is formed on a substrate with spacing therebetween. The first lens-base elements are heated so that the first lens-base elements melt to form first lenses having round surfaces. A separation layer is formed to cover the first lenses and the substrate. A second array of second lens-base elements is formed, the second lens-base elements being placed on a region where the first lenses are not formed so as to partly overlap with the first lenses. The second lens-base elements are also heated so that the second lens-base elements melt to form second lenses having round surfaces. The lens array comprises the substrate and the first and second lenses.

This is a division of application Ser. No. 08/176,440, filed on Jan. 3,1994 now U.S. Pat. No. 5,536,445.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method of manufacturing a lens array,particularly a microlens array having a plurality of microlensesarranged two-dimensionally or one-dimensionally, and further to the lensarray and application thereof.

2. Description of the Related Art

Characteristics required for each lens in a lens array are a focusingfunction of focusing light on a point and light utilization efficiency.

One of techniques for fabricating a lens array is a melting method (see,Zoran et al. "Technique for monolithic fabrication of microlens arrays",APPLIED OPTICS, Vol. 27, No. 7, 1 Apr., 1988, pp 1281-1284). Accordingto this technique cylinders are formed using photoresist on circularpedestals and are heated. The cylinder material melts and flows to thepedestal to form the array of spherical microlenses.

The microlenses have spherical surfaces so that a good focusing functionis obtained. However since the apertures of the microlenses are circles,the arrangement has spacing between the microlenses. The upper limit oflight utilization efficiency is almost 80%.

SUMMARY OF THE INVENTION

An object of the present invention is to achieve both a good focusingfunction and high light utilization efficiency.

Another object of the present invention is to provide a method ofmanufacturing a lens array achieving the above objectives.

Still another object of the present invention is to provide a lens arrayachieving the above objectives and application of the lens array.

A method of manufacturing a lens array according to the presentinvention comprises the steps of: forming a first array of firstlens-base elements on a substrate with spacing therebetween; heating thefirst lens-base elements so that the first lens-base elements melt toform first lenses; forming a second array of second lens-base elementsin a place lacking of the first lenses so as to partly overlap with thefirst lenses; and heating the second lens-base elements so that thesecond lens-base elements melt to form second lenses.

The steps of forming and heating the second lens-base elements arerepeated, if necessary.

In order to protect the first lenses in the heating step for forming thesecond lenses, a separation layer for covering the first lenses and thesubstrate is formed in one embodiment of the present invention.

According to another embodiment of the present invention, a material ofthe second lens-base elements different from that of the first lens-baseelements is used.

In still another embodiment of the present invention, a replica of thelens array having at least the first lenses is made and the secondlens-base elements are formed on the replica.

According to the present invention, the shape of the lenses may be acircle, an ellipse or other arbitrary shapes.

Since the shape of the lenses can be a circle, the lenses have sphericalsurfaces. Since the first lenses have spherical surfaces and the secondlenses partly overlap with the first lenses, the second lenses also havespherical surfaces. An aberration is small and a good light focusingfunction is obtained.

The second lenses partly overlap with the adjacent first lenses.Accordingly there are no spaces or gaps where a lens is not disposed orthe space can be very small. Light utilization efficiency of about 100%can be achieved.

Other features and advantages of the present invention will be apparentfrom the following description taken in conjunction with theaccompanying drawings, in which like reference characters designate thesame or similar parts throughout the figures thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1a to 1i show processes for fabricating a lens array;

FIGS. 2a to 2e are perspective views for showing processes offabricating the lens array;

FIG. 3 shows a standard arrangement of a two-dimensional lens array;

FIG. 4 is a plane view of a one-dimensional lens array;

FIG. 5 is a plane view of another one-dimensional lens array;

FIG. 6 is a longitudinal sectional view of the one-dimensional lensarray shown in FIG. 4 or 5;

FIG. 7 is a perspective view of a one-dimensional lens array;

FIG. 8 is a sectional view of the one-dimensional lens array shown inFIG. 7;

FIG. 9 is a sectional view of another one-dimensional lens array;

FIG. 10 is a sectional view of still another one-dimensional lens array;

FIG. 11 is a perspective view for showing a boundary line betweenadjacent lenses;

FIG. 12 also shows boundary lines among lenses;

FIGS. 13a to 13e show examples of arrangements of lenses.

FIG. 14 shows an example of an arrangement of lens apertures;

FIG. 15 shows an example of an arrangement of lens apertures;

FIG. 16 shows an example of an arrangement of lens apertures;

FIG. 17 shows an example of an arrangement of lens apertures;

FIG. 18 shows an example of an arrangement of lens apertures;

FIG. 19 shows an example of an arrangement of lens apertures;

FIG. 20 shows an example of an arrangement of lens apertures;

FIG. 21 is a sectional view showing an imaging apparatus;

FIG. 22 is a sectional view showing a display apparatus;

FIG. 23 is a sectional view showing an image forming device;

FIG. 24 is a partially cut-away perspective view showing an opticalinformation processing device; and

FIG. 25 is a partially cut-away perspective view showing an opticalcoupling device.

DESCRIPTION OF THE PREFERRED EMBODIMENT

Two-Dimensional Lens Array (Standard Type)

Process steps for fabrication of a two-dimensional microlens array areschematically depicted in FIGS. 1a to 1i. Intermediate products and afinal product in some process steps are illustrated in FIGS. 2a through2e, in which all of lens-base elements and lenses are not illustrated,but only a representative part of them is depicted.

At the first step, a film or layer of photo-sensitive synthetic resin,for example, a positive photoresist 11B is formed on a substrate 10(e.g., SiO₂ (glass) or Si substrate) by spin coating (see FIG. 1a).

Next, a mask 14 is placed on or above the positive photoresist layer 11Band the photoresist layer 11B is exposed by light through openingsformed on the mask 14 (see FIG. 1b). The mask 14 has portions forshielding the light, the portions having a shape corresponding to thelens-base elements to be formed.

By developing the photoresist, the lens-base elements 11A made of thephotoresist remain on the substrate 10. The lens-base elements 11A are athin and cylindrical shape (see FIGS. 1c and 2a). The lens-base elements11A are exposed to near ultraviolet (UV) radiation to lower the meltingtemperature of the elements, if necessary.

The substrate 10 and the lens-base elements 11A are heated or baked toabove the melting temperature of the photoresist material, e.g., to 140°C. or 150° C. The material of the lens-base elements melts to form thefirst spherical microlenses 11 (see FIGS. 1d and 2b). The upper surfaceof the molten material is rounded due to the surface tension of themolten material but does not flow due to the surface tension. Thediameter of the microlens 11 is the same as that of the lens-baseelement 11A. However, the diameter of the microlens 11 may be largerthan that of the lens-base element 11A depending on the temperaturecondition, especially when the temperature becomes higher. Anyway thediameter of the microlens 11 is controllable.

For convenience of explanation, first parallel dot-and-dash lines (firstpartitioning center lines) at a first constant interval (a pitch P), andsecond parallel dot-and-dash lines (second partitioning center lines) atthe same interval (a pitch P) as the first interval are assumed andillustrated in FIGS. 2a to 2e, the first lines are perpendicular to thesecond lines. The lens-base elements 11A are so positioned that thecenter of the elements 11A coincide with the intersecting points (node)of the first and second lines. The lens-base elements 11A disposed alongone line are so arranged that the elements 11A are positioned on everyother intersecting points. The lens-base elements 11A disposed along oneline are shifted from the lens-base elements 11A disposed along anotherline adjacent to said one line by one pitch P.

The diameter r of the lens-base element 11A is larger than the pitch P,but the lens-base elements 11A adjacent to each other are not made intocontact with each other as described later. That is, each of theelements 11A are isolated from one another. There are spaces or gapsbetween the adjacent elements 11A. The same is true of the lenses 11.

After formation of the first microlenses 11, a separation layer or film(intermediate layer or film) 16 is formed to cover the first lenses 11and the upper surface of the substrate 10 (see FIGS. 1e and 2c). Forexample, the separation layer 16 is formed by accumulating inorganicmaterial such as SiO₂, Cr by sputtering or deposition technology. Thethickness of the layer 16 is less than about 1 μm.

A photo-sensitive synthetic resin (e.g., positive photoresist) layer 12Bis formed on the separation layer 16 (see FIG. 1f). This layer 12B maybe made of the same material as that of the layer 11B.

The positive photoresist layer 12B is subject to exposure through mask15 having square light-shielding portions (see FIG. 1g).

After development of the second photoresist 12B on the separation layer18, second lens-base elements 12A having thin square pillar shapesappear (see FIGS. 1h and 2d). As seen from FIG. 2d, the lens-baseelements 12A are positioned at the intersecting points of the first andsecond lines where no first lenses 11 exist and the center of theelements 12A coincide with the intersecting point. The length L of aside of square element 12A is almost same as the pitch P. Side portionsof the elements 12A overlap with the peripheral portions of the firstlenses 11.

Finally, the elements 12A (and the lenses 11 and the substrate 10) areheated or backed. The lens-base elements 12A melt to form secondmicrolenses 12 (see FIGS. 1i and 2e). The second microlenses 12 havealso round and spherical surfaces.

The separation layer 16 has the function of protecting and keeping theshape of the first lens 11 in the processes of coating, exposure,development and melting of the second photoresist. The separation layershould be made of materials, which cannot be molten in the meltingprocess of the second lens-base elements.

The first lenses 11 and second lenses 12 are overlapped to each other attheir peripheral portions, and the substrate 10 is entirely covered bythe first and second lenses 11, 12 (except for peripherals of thesubstrate). There are no portions that lack the lens function on thesubstrate 10, so that light utilization efficiency of about 100% isachieved.

The height of the first photoresist 11B is so determined so as to obtainthe first lenses 11 having a desired thickness. The height of the secondphotoresist 12B is so determined so as to obtain the second lenses 12having the same thickness as that of the first lenses 11.

Photolithography technique is utilized to fabricate the first and secondlens-base elements in the above embodiment. However other techniquessuch as electron-beam (EB) lithography may be used, as well.

The two-dimensional lens array as described above can be used as is. Inthis case, transparent materials are used as the materials of thesubstrate, photoresist and separation layer.

Mass production is possible using a molding method that employs a mold(an injection molding method or molding method using a resin that ishardened by UV radiation).

Processes for manufacturing a stamper and for a two-dimensional lensarray with use of the stamper are explained briefly hereinafter.

A nickel film is fabricated on the above described two-dimensional lensarray serving as a master plate by use of an electroforming method. Themaster plate is then removed to obtain a nickel stamper comprising thenickel film. The nickel stamper has concaves corresponding to the firstand second lenses 11, 12.

Subsequently, a molten UV-setting resin is filled between the nickelstamper and a transparent substrate and then the nickel stamper and thesubstrate are depressed against each other. An ultraviolet ray isirradiated through the transparent substrate to solidify the UV-settingresin.

After the resin becomes stiff, the stamper is removed, thereby obtaininga two-dimensional lens array made of the UV-setting resin, formed on thetransparent substrate and having the same configuaration as that of thetwo-dimensional lens array shown in FIGS. 1i and 2e.

In summary, the two-dimensional lens array shown in FIGS. 1i and 2e isfabricated by the first and second melting stages, the melting stageincluding a process of patterning the lens-base elements (byphotolithography or EB lithography) and e process of melting thelens-base elements (by heating). The lens-base element 11A in the firstmelting stage has a circular shape when viewed from a plane, whereas thelens-base element 12A in the second melting stage has a square shapewhen viewed from a plane. The plane view of the lens-base element iscalled a lens aperture in this specification.

FIG. 3 shows a general configuaration of lens apertures in thetwo-dimensional lens array. A pitch in one direction is P1 and a pitchin another direction perpendicular to the one direction is P2. FIGS. 2ato 2e show a special case where P1 is equal to P2.

The first lens aperture 11a in the first melting stage is formed to be acircle or almost circular shape. The lens apertures 11a should cover atleast the length of shorter pitch, and be isolated from one another asdescribed above. Accordingly, the diameter r of the lens aperture 11a isdefined as follows:

    MIN  P1, P2!<r<(P1.sup.2 +P2.sup.2).sup.1/2                Eg. (1)

An operation MIN is one to select the smaller one of P1 and P2. Thecenter of the circular lens aperture 11a is positioned on or near theintersecting point of the first and second partitioning center lines.

The second lens aperture 12a (indicated by hatching) in the secondmelting stage is formed to be a rectangle or rectangular shape withcorners cut off. The lengthes L1 and L2 of sides of the rectangle lensaperture 12a are set to be equal to or nearly equal to P1 and P2,respectively, in order that the second lens overlaps with the first lensat their peripheral portions.

With above conditions, a two-dimensional lens array comprising aplurality of first and second lenses arranged regularly without gapshaving no lenses occupies is obtained.

One-Dimensional Lens Array (Row of Lenses)

FIGS. 4 and 5 show examples of a one-dimensional lens array (a row oflenses). A plurality of microconvex lenses 11 and 12 are arranged in arow on a substrate 10 in FIG. 4. A plurality of micro-cylindrical lenses11 and 12 are arranged in a row on a substrate 10 in FIG. 5. FIG. 6 isan enlarged cross sectional view taken along a center line of the row oflenses shown in FIG. 4 or 5.

In these figures the first lenses 11 disposed in every other positionsare fabricated in the first melting stage. That is, the first lens-baseelements are formed by photolithography with use of a firstphoto-sensitive material, e.g., a negative photoresist. The lens baseelements then are melted by baking them.

The second lenses 12 are fabricated in the second melting stage. Thesecond lens-base elements are formed by photolithography. The secondlens-base elements are made of a second photo-sensitive material whichis different from the first photo-sensitive material, e.g., a positivephotoresist, so that the first lenses 11 are not affected in the processof development of the second lens-base elements, and the first lenses 11and the second lenses 12 are not mixed with each other when the secondlens-base elements are melted to form the second lenses 12 even if thesecond lens-base elements contact with the first lenses 11.

In this way, a row of lenses in which a plurality of lenses are arrangedin a row without any gap therebetween is manufactured with two meltingstages.

In a case where circular shaped concave lenses as shown in FIG. 4 arefacricated, both the first and second lens-base elements are formed likea thin cylinder in shape.

FIGS. 7 and 8 show another example of a one-dimensional lens array. Thefirst lenses 11 and second lenses 12 are overlapped to each other attheir peripheral portions. The lens aperture of the first lenses 11 is acircle. The lens aperture of the second lenses 12 has a shape obtainedby cutting straightly overlapped portions from a circle. The shape orform of the second lens aperture (and the third lens aperture when thethird melting stage is necessary) will be exlained theoretically later.

It goes without saying that the one-dimensional lens array shown inFIGS. 4 to 8 are used as master plates to make stampers which are usedin mass production of one-dimensional lens arrays.

Further the method of fabricating one-dimensional lens arrays shown inFIGS. 4 to 8, in which different materials are used for the first andsecond lenses, is applicable to the fabrication of the two-dimensionallens array as shown in FIGS. 1a to 3.

FIG. 9 shows a further example of a one-dimensional lens array. Aseparation layer 18 is used to protect the first lenses 11.

FIG. 10 shows still another example of a one-dimensional lens array. Theprocesses for fabricating this lens array are as follows:

After first lenses are formed on a first substrate, the first substratewith the first lenses is used as a master plate to make a nickelstamper. A molten resin, e.g., acrylic (acryl)-resin, is injectedbetween the stamper and a second substrate and the resin is solidifiedby photo polymerization. A replica 17 made of the acrylic resin andhaving first lens portions 17A is obtained by removing the stamper andthe second substrate.

Second lens-base elements are formed on the replica 17 at positionsbetween the first lens portions 17A and are subject to the secondmelting process to be second lenses 12. The replica 17 is not molten inthe second melting process.

The lens array thus fabricated may be used as is, and also may be usedas a master plate for making a stamper with which another replica havingfirst and second lens portions is manufactured.

The method of making the lens array as shown in FIG. 10 with the replicahaving the first lens portions is also applied to processes for making atwo-dimensional lens array.

Theoretical Explanation and Various Arrangements

A boundary line (boarder line) between two lenses which are adjacent toand partly overlapped to each other is discussed hereinafter.

As shown in FIG. 11, the boundary line Q1 in the bottom surfaces of thelenses 11 and 12 is ideally or desirably perpendicular at midpoint(perpendicular bisector) of a line (segment) which is drawn between acenter point 01 of the lens 11 and a center point 02 of the lens 12. Theboundary line BL in the upper surfaces of the lenses 11 and 12 is in aplane QS1 (hatched) which rises on the perpendicular bisector Q1vertically to the bottom surfaces. The lens 11 formed in the firstmelting stage acts as a pedestal for regulating the height of the secondlens 12 and the height of both lenses 11 and 12 becomes equal to eachother at the boundary line BL. If both lenses 11 and 12 are ideallyformed, they have no aberration or less aberration so that a goodfocusing function is achieved. This is the reason why the secondlens-base elements 12A shown in FIGS. 1h and 2d are formed to have thinsquare pillar shapes.

FIG. 12 shows a first lens aperture 11a, second lens aperture 12a andthird lens aperture 13a when a two dimensional lens array is fabricatedthrough triple melting stages.

The lens aperture 11a of the first melting stage is a circle. The lensaperture 12a of the second melting stage (indicated by hatching) has ashape of a circle with a cutoff defined by a boundary line Q1 which is aperpendicular bisector of a segment between the center points 01 and 02of the aperture 11a and 12a. The lens aperture 13a of the third meltingstage (hatched doubly) is formed to be a circle having two cutoffs. Thefirst cutoff is formed by cutting the circle along a boundary line Q2which is a perpendicular bisector of a segment between the center points01 and 03 of the apertures 11a and 13a. The second cutoff is formed bycutting the circle along a boundary line Q3 which is a perpendicularbisector of a segment between the center points 02 and 03 of theapertures 12a and 13a. As described above the lens apertures 11a, 12aand 13a are plane views of the lens-base elements of the first, secondand third melting stages.

FIGS. 13a to 13e show examples of arrangements (arrays) of lenses. Thesefigures do not intend to indicate shapes (contours) of lens apertures,but just show ways of arrangements of lenses.

FIG. 13a shows a regular arrangement or a so-called mosaic arrangement.

FIGS. 13b, 13c, 13d and 13e show a so-called delta arrangement(so-called triangle-type arrangement or zigzag pattern).

The two-dimensional lens array shown in FIG. 3 is of the mosaicarrangement.

Another example of a two-dimensional lens array of the mosaicarrangement is shown in FIG. 14.

The first lens aperture 11a is an ellipse in which the major axis islonger than the longer pitch P2 and the minor axis is longer than theshorter pitch P1. However the first lens apertures 11a are isolated fromone another. The second lens aperture 12a is a rectangle or rectanglarshape with corners cut off. The lengthes L1 and L2 of the sides of theaperture 12a are equal to the pitches P1 and P2, respectively.

Each lens of the array shown in FIG. 14 has the characteristics ofastigmatism. The lenses are arranged with no gap (or space) or small gaptherebetween.

FIG. 15 shows a two-dimensional lens array of the delta arrangementdepicted in FIG. 13b.

This two-dimensional lens array is made by triple melting stages. Theboundary lines of the apertures 11a, 12a and 13a are determined asexplained with reference to FIGS. 11 and 12.

The first lens aperture 11a is a circle. The diameter of a circledefining the first lens aperture 11a is larger than a diameter of acircle which contacts with the second and third lens apertures 12a and13a and is smaller than a diameter of a circle which does not contactwith each other.

The diameter D of the circle defining the first lens aperture 11a isexpressed as follows:

    MIN  D0, D1!<D<D2                                          Eg. (2)

where

D0: a diameter of a circle which contacts with the second and thirdapertures in a direction of the shorter pitch P1.

D1: a diameter of a circle which contacts with the third aperture in adirection of the larger pitch P2, and

D2: a diameter of a circle which contacts which another circle of thesame diameter.

That is,

    D0=P1                                                      Eg. (3)

    D1= (P1/2).sup.2 +P2.sup.2 !.sup.1/2                       Eg. (4)

    D2= (3P1/2).sup.2 +P2.sup.2 !.sup.1/2                      Eg. (5)

The shape (contour) of the second lens aperture 12a comprises arcs andstraight lines. The arcs are portions of a circle which has almost thesame diameter of the circle defining the first lens aperture 11a and aredrawn in a region where the second lens aperture 12a does not overlapwith the first lens aperture 11a. The straight lines are drawn in aregion where the second lens aperture 12a overlaps with the first lensaperture 11a. The straight lines are the boundary lines between thefirst and second lens apertures 11a and 12a, each of which connects bothends of the arcs.

The shape (or contour) of the third lens aperture 13a is a hexagon thevertexes of which are on the boundary lines between the first and thesecond lens apertures 11a and 12a.

The advantageous features of the lens array shown in FIG. 15 are thatthere is no gap (space) among lenses and the lenses show no aberrationor less aberration.

This lens array is made by several methods.

A first method is to utilize a seperation layer twice. That is, afterthe first lenses are formed in the first melting stage, the first lensesare covered by a first separation layer. Then the second lenses areformed in the second melting stage. Thereafter the second lenses and thefirst separation layer are covered by a second separation layer.Finally, the third lenses are fabricated in the third melting stage.

A second method is that which utilizes a replica and a separation layer.The replica comprises a substrate portion and first lens potirons formedon the substrate portion integral therewith. The second lenses areformed on the replica in the second melting stage. After the secondlenses are covered by a separation layer, the third lenses are formed inthe third melting stage.

In the third method, a replica having first lens portions and secondlens portions is formed. The third lenses are fabricated on the replica.

It goes without saying that replicas are manufactured using as a masterplate the lens array fabricated by the above discussed methods.

Another example of a two-dimensional lens array of the delta arrangementdepicted in FIG. 13b is shown in FIG. 16.

The first lens aperture 11a is an ellipse. The second lens aperture 12acomprises arcs which are defined by portions of an ellipse and straightlines serving as boundary lines. The other features of this lens arrayare the same as those of the lens array shown in FIG. 15. The lenses areof astigmatism.

FIG. 17 shows a two-dimensional lens array of a type of the deltaarrangement depicted in FIG. 13c. This lens array is constituted byarranging a plurality of the one-dimensional lens arrays shown in FIG. 7in parallel.

The first lens aperture 11a is a circle which has such a diameter thatthe first lens apertures overlap (contact) with the second lensapertures 12a, but do not overlap (contact) with each other. Thediameter D of the first lens aperture 11a is expressed as follows:

    D0<D<D1                                                    Eg. (6)

where

    D0=P1,                                                     Eg. (7)

and

    D1= (P1/2).sup.2 +P2 .sup.2 !.sup.1/2tm Eg. (8)

The second lens aperture 12a comprises arcs and straight lines. The arcsare part of a circle having almost the same diameter as that of thefirst lens aperture 11a. The straight lines define the boundariesbetween the first and second lens apertures 11a and 12a, each of whichconnects ends of the arcs.

There is a very small spacing or gap between the rows of lenses. Ofcourse, the spacing is not necessarily needed. However this arrangementhas an advantage that the two-dimensional lens array is fabricated bytwo melting stages in comparison with the arrangement shown in FIG. 15.

FIG. 18 shows another example of a two-dimensional lens array of thedelta arrangement depicted in FIG. 13c.

The first lens aperture 11a is an ellipse, the size of the first lensaperture is so determined that the first lens aperture 11a overlaps(contact) with the second lens aperture 12a, but the first lensapertures 11a do not contact with each other. That is, the minor axis aand major axis b are defined as follows:

    a>P1                                                       Eg. (9)

    b<(2aP2)/ 4a.sup.2 -P1.sup.2 !                             Eg. (10)

The second lens aperture 12a is constituted by arcs which are parts ofan ellipse the size of which is almost same as that of the first lensaperture, and straight lines defining the boundaries between the firstand second lens apertures 11a and 12a, each of which connects ends ofthe arcs.

The lenses of this two-dimensional lens array have a nature ofastigmatism.

A two-dimensional lens array shown in FIG. 19 has a delta arrangement asdepicted in FIG. 13e.

The first lens aperture 11a has a shape of a circle. The size of thecircle is determined such that the first lens apertures 11a partlyoverlap (contact) with the second lens apertures 12a but the first lensapertures are not made to contact with each other. This condition isexpressed as follows:

    D0<D<D1                                                    Eg. (11)

where D is a diameter of the circle defining the contour of the firstlens aperture 11a, and

    D0= (P1/2).sup.2 +P2.sup.2 !.sup.1/2                       Eg. (12)

    D1=P1                                                      Eg. (13)

The second lens aperture 12a has a shape like a rhombus, constituted byarcs and straight lines. Arcs are parts of a circle having almost thesame diameter as that of the circle defining the first lens aperture andare drawn in a region outside the first lens aperture 11a. The straightlines appear in the region inside the first lens aperture 11a andconnect ends of the arcs. The straight lines are boundary lines betweenthe first and second lens apertures 11a and 12a.

The remarkable features of this arragement are that a spacing (gap)between the first lens apertures or between the second lens apertures isvery small, and that the lenses have no aberration or less aberrationand that two melting stages are enough to fabricate this lens array.

FIG. 20 shows an another structure of a two dimensional lens array of atype of the delta arrangement shown in FIG. 13c or 13e.

A point which is different from the feature shown in FIG. 19 is that thefirst lens aperture is an ellipse. The lens array includes lenses whichproduce astigmatism.

Applications of a One- or Two-Dimensional Lens Array

Many applications of the one- or two-dimensional lens arrays describedabove are conceivable.

FIG. 21 schematically illustrates an imaging device.

A charge-coupled device (CCD) 40 includes many photodiode elements 41and electrodes 42 for driving the CCD 40. The arrangement of thephotodiode elements 41 may be the regular (mosaic) arrangement or deltaarrangement. One type of the two-dimensional lens arrays described abovesuitable for the arrangement of the photodiode elements is used. Thetwo-dimensional lens array 30 is disposed on the CCD 40 via anintermediate transparent layer 43 therebetween. Each of the lenses ofthe lens array 30 corresponds to each of the photodiode elements 41 ofthe CCD 40.

Application of the two-dimensional lens array to a light-crystal panelis depicted in FIG. 22. As well known, a liquid-crystal panel 43comprises two glass substrates 44 arranged with a small spacingtherebetween and a liquid-crystal 45 filling the gap between the glasssubstrates 44. Scanning electrodes, signal electrodes andlight-shielding films 46 (these are assigned to same reference numeralfor convenience) are formed on the surfaces of the glass substrates 44.A region enclosed by these electrodes 46 is called a pixel (or anaperture). A pixel electrode is not shown. The lens array 30 is disposedso as to face the liquid-crystal panel 43 and each microlens of the lensarray 30 corresponds to the pixel of the liquid-crystal panel 30.

FIG. 23 shows an image forming device using three two-dimensional (orone-dimensional) lens arrays 30 to form an erect image.

FIG. 24 shows an optical information processing device with use oftwo-dimensional lens arrays.

A spatial modulating device or memory 50 includes a plurality ofopenings or light receiving elements 51 on one surface thereof and aplurality of openings or light emitting elements 52 on the other surfacethereof, these openings or elements being arranged in a mosaic or deltaarrangement. Two lens arrays 30A and 30B are disposed above and belowthe device 50. The lenses of the lens arrays 30A and 30B correspond tothe openings or elements 51 and 52. Light focused by the lens of thelens array 30A impinges upon the corresponding opening or element 51 ofthe device 50. Light emitted from the opening or element 52 iscollimated by the corresponding lens of the lens array 30B.

FIG. 25 shows an optical coupling device using one-dimensional lensarrays.

Light beams outputted from optical fibers 60A supported by a support 61Aare collimated by the lenses of the lens array 30A. The collimated lightbeams are focused by the lenses of the lens array 30B to be coupled tothe optical fibers 60B fixed to a support 61B.

Further the one- or two-dimensional lens array is used as an opticalcoupling device for coupling light beams between an array of lightemitting elements or light receiving elements and space. For example,many light emitting elements can be arranged on a boardtwo-dimensionally. The light beams emitted from the elements are coupledto lenses of a two-dimensional lens array to be collimated thereby.

As many apparently widely different embodiments of the present inventioncan be made without departing from the spirit and scope thereof, it isto be understood that the invention is not limited to the specificembodiments thereof except as defined in the appended claims.

What is claimed is:
 1. A lens array manufactured by the method comprising the steps of:forming a first array of first lens-base elements on one side of a substrate with spacing therebetween; heating the first lens-base elements so that the first lens-base elements melt to form first lenses on the one side of the substrate; covering the first lenses and the substrate with a first separation layer; forming a second array of second lens-base elements in a region on the one side of the substrate where the first lenses are not formed so as to partly overlap with the first lenses; and heating the second lens-base elements so that the second lens-elements melt to form second lenses substantially adjacent to the first lenses on the one side of the substrate.
 2. A lens array manufactured by the method comprising the steps of:forming a first array of first lens-base elements on one side of a substrate with spacing therebetween; heating the first lens-base elements so that the first lens-base elements melt to form first lenses on the one side of the substrate; forming a second array of second lens-base elements with a material different from that of the first lens-base elements in a region on the one side of the substrate where the first lenses are not formed so as to partly overlap with the first lenses; and heating the second lens-base elements so that the second lens-base elements melt to form second lenses substantially adjacent to the first lenses on the one side of the substrate.
 3. A lens array manufactured by the method comprising the steps of:forming a first array of first lens-base elements on one side of a substrate with spacing therebetween; heating the first lens-base elements so that the first lens-base elements melt to form first lenses in a lens array on the one side of the substrate; making a replica of the lens array having the first lenses; forming a second array of second lens-base elements on the replica in a region on one side of the replica where first lens portions of the replica are not formed so as to partly overlap with the first lens portions of the replica; and heating the second lens-base elements so that the second lens-elements melt to form second lenses substantially adjacent to the first lens portions on the one side of the replica.
 4. A lens array manufactured by the method comprising the steps of:forming an array of lens-base elements on one side of a substrate with spacing therebetween; heating the lens-base elements so that the lens-base elements melt to form lenses on the one side of the substrate; and repeating the steps of forming and heating the lens-base elements a second time such that additional lens-base elements and additional lenses are formed on the one side of the substrate in a region where the lenses are not formed so as to be substantially adjacent to and to partly overlap with the lenses formed on the one side of the substrate.
 5. A lens array manufactured by the method comprising the steps of:forming a first array of first lens-base elements on one side of a substrate with spacing therebetween; heating the first lens-base elements so that the first lens-base elements melt to form first lenses on the one side of the substrate; forming a second array of second lens-base elements in a place on the one side of the substrate lacking the first lenses so as to partly overlap with the first lenses; heating the second lens-base elements so that the second lens-base elements melt to form second lenses on the one side of the substrate; and repeating the steps of forming and heating the second lens-base elements, if necessary.
 6. A lens array manufactured by the method comprising the steps of:forming a first array of first lens-base elements on one side of a substrate with spacing therebetween; heating the first lens-base elements so that the first lens-base elements melt to form first lenses on the one side of the substrate; forming a second array of second lens-base elements in a place on the one side of the substrate lacking the first lenses so as to partly overlap with the first lenses; heating the second lens-base elements so that the second lens-base elements melt to form second lenses on the one side of the substrate; repeating the steps of forming and heating the second lens-base elements, if necessary, thereby making a first lens array on the one side of the substrate; accumulating a stamper material on said first lens array serving as a master plate to form a stamper; peeling the stamper from the master plate; filling the stamper with a molten resin; solidifying the resin in the stamper; and removing the stamper to obtain a second lens array made of the resin.
 7. A lens array comprising:a substrate; a first array of first lenses arranged on one side of said substrate with spacing portions therebetween on the one side of said substrate; and a second array of second lenses disposed on the spacing portions of the one side of said substrate between the first lenses, the second lenses partly overlapping with the adjacent first lenses on the one side of said substrate.
 8. The lens array according to claim 7 further comprising:a third array of third lenses disposed on spacing portions lacking the first lenses and the second lenses on the one side of said substrate, the third lenses partly overlapping with the adjacent first and second lenses on the one side of said substrate.
 9. The lens array according to claim 7 wherein the lens array is a two-dimensional lens array.
 10. The lens array according to claim 7 wherein the lens array is a one-dimensional lens array.
 11. An imaging apparatus with use of the lens array as defined in claim 7 comprising:an imaging device having a plurality of photo-sensitive elements; and the lens array disposed so as to face the imaging device, each lens of the lens array corresponding to each photo-sensitive elements.
 12. A display apparatus of dot-matrix type with use of the lens array as defined in claim 7 comprising:a display device of dot-matrix type having an array of display elements; and the lens array disposed so as to face the display device, each lens of the lens array corresponding to each display element.
 13. An image forming device including the lens array as defined in claim
 7. 14. An optical information processing apparatus with use of the lens array as defined in claim 7 comprising:a plurality of optical modulating elements; and the lens array the lenses of which correspond to the optical modulating elements.
 15. An optical coupling device with use of the lens array as defined in claim 7 comprising:a plurality of light input/output portions; and the lens array the lenses of which correspond to the light input/output portions.
 16. The lens array according to claim 7, wherein the adjacent first and second lenses are substantially formed in a plane, said lenses substantially covering said substrate on the one side of said substrate and having round surface portions which are exposed to incident light, wherein the light incident on said plane is refracted on said round surface portions.
 17. The lens array according to claim 8, wherein the adjacent first, second, and third lenses are substantially formed in a plane, said lenses substantially covering said substrate on the one side of said substrate and having round surface portions which are exposed to incident light, wherein the light incident on said plane is refracted on said round surface portions. 